Solve for $x$ : $ 4|x + 10| + 4 = 6|x + 10| + 10 $
Explanation: Subtract $ {4|x + 10|} $ from both sides: $ \begin{eqnarray} 4|x + 10| + 4 &=& 6|x + 10| + 10 \\ \\ {- 4|x + 10|} && {- 4|x + 10|} \\ \\ 4 &=& 2|x + 10| + 10 \end{eqnarray} $ Subtract $10$ from both sides: $ \begin{eqnarray} 4 &=& 2|x + 10| + 10 \\ \\ {- 10} && {- 10} \\ \\ -6 &=& 2|x + 10| \end{eqnarray} $ Divide both sides by ${2}$ $ \dfrac{-6} {{2}} = \dfrac{2|x + 10|} {{2}} $ Simplify: $ -3 = |x + 10| $ The absolute value cannot be negative. Therefore, there is no solution.